СОВРЕМЕННАЯ ЭЛЕКТРОДИНАМИКА
MODERN ELECTRODYNAMICS ISSN 2949-0553
Contents
Section 1. Topics on theoretical electrodynamics
Calculation of self-induction a thin cylindrical metal wire
E.V. Zavitaev, O.V. Rusakov, A.I. Utkin, K.E. Kharitonov
Abstract
The article presents an analytical calculation of the self-induction of a thin cylindrical wire made of a non-magnetic metal. The general case is considered, where the ratio of the mean free path of electrons to the radius of the wire can take arbitrary values. The work is based on a rigorous kinetic approach, which is based on solving the Boltzmann kinetic equation for conduction electrons in a metal. The boundary conditions used are the conditions of mirror-diffuse reflection of electrons from the inner surface of the wire (Fuchs model). Within the framework of the problem statement, a high-frequency current is excited in the wire by a uniform time-periodic electric field without taking into account the macroscopic skin effect. The sought-for self-inductance coefficient is calculated through the energy of the magnetic field and the current flowing through the cross-section of the wire. As a result of the calculation, it was found that the self-induction of a thin cylindrical metal wire significantly depends on the ratio of its radius to the mean free path of electrons, the coefficient of reflectivity of its surface, and the frequency of the external electric field. The complex physical nature of self-induction at microscopic scales was also substantiated. The obtained results clearly demonstrate important kinetic and dimensional features of small conducting systems that are not observed in macroscopic samples and can be used in the design of components for modern micro- and nanoelectronics.
Keywords: thin wire, magnetic field energy, magnetic induction, self-induction, current density
Section 2. Topics on computer simulation in electrodynamics
The method of moments application for the numerical solution of the diffraction problem in a thin perfectly conducting wire
I.S. Khuzin, D.A. Konyaev
Abstract
This paper examines the application of the method of moments to solve the problem of electromagnetic wave diffraction by an arbitrarily bent thin perfectly conducting wire of finite length significantly exceeding its cross-sectional diameter. An Electric Field Integral Equation (EFIE) is considered in the thin-wire approximation, which is solved for current using the projection method. Finite elements of zero, first, and second orders (piecewise constant, linear, and quadratic) are used as basis and test functions. A numerical code implementing the Method of Moments solution for diffraction by such wires has been developed. Particular attention is given to the numerical calculation of the integrals arising during the assembly of the system matrix and the treatment of the case when source and receiver segments coincide. Calculations for wires of various configurations are compared with the results obtained using the FEKO software package. The necessity of using the processing of the case of coincidence of the source and receiver segments for small wire radii is demonstrated. Numerical experiments highlight the shortcomings of low-order basis functions: finite zero-order elements often do not allow achieving acceptable accuracy in computing the current induced on the wire, which is noticeable in small models when using meshes with a small number of segments. It is also shown that the use of first‑order finite elements is preferable in terms of both the accuracy of the results and the computational efficiency.
Keywords: method of moments, electromagnetic wave diffraction, thin perfectly conducting wire, Electric Field Integral Equation (EFIE), finite element method
Section 3. Topics on experimental electrodynamics
A.V. Kiselev, A.V. Gusev, A.V. Gluschenkov, S.A. Kositsyn, D.I. Surov, O.P. Bazhenova, E.V. Rykov, A.O. Shtokal
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